Radiation Patterns of Rossby Waves in Wind/Currents

The geometry of the wave normal curves for Rossby waves in the presence of winds plays an important role in describing the radiation pattern generated by a time harmonic, spatially compact source. The Doppler shifted frequency not only distorts the classical Longuet-Higgins offset wave normal circle but also introduces a new branch consisting of a plane with a bump corresponding to waves convected with the wind. The method of stationary phase demonstrates that the reciprocal polar to these curves provides the radiation patterns. We present a number of these interesting patterns for the cases of zonal and meridional winds.